Lessons from the long flow records of the Nile: determinism vs indeterminism and maximum entropy

D. Koutsoyiannis, and A. Georgakakos, Lessons from the long flow records of the Nile: determinism vs indeterminism and maximum entropy, 20 Years of Nonlinear Dynamics in Geosciences, Rhodes, Greece, doi:10.13140/RG.2.2.10996.14727, 2006.



Three long records of the Nile River are analyzed. The first is the 131-year long contemporary record of monthly flows at Aswan (1870-2001). The other two are the records of annual maximum and minimum water levels from the Roda Nilometer for an 813-year period (640-1452). These records compose the longest instrumental data set available worldwide and their importance in understanding and modelling hydroclimatic behaviours is obvious. Spectral and chaotic dynamical analyses of all records do not provide clear evidence of deterministic signatures except for the obvious annual periodicity. Stochastic analysis suggests that all records have virtually identical long-term behaviour characterized by long-range dependence with Hurst coefficient around 0.85 both on annual and monthly basis. Notably, the long term behaviour departs from simple scaling in a manner that implies uncertainty on large time scales even higher than that of simple scaling, which is known to be already very high compared to typical short-range dependence processes. An explanation of the observed long-term behaviour is sought based on the principle of maximum entropy. Maximization of entropy both on local and global temporal setting produces a dependence structure that is asymptotically (i.e. for large time scales) scaling and seems to be in accordance with the observed behaviour of the Nile records.

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See also: http://dx.doi.org/10.13140/RG.2.2.10996.14727

Our works that reference this work:

1. D. Koutsoyiannis, H. Yao, and A. Georgakakos, Medium-range flow prediction for the Nile: a comparison of stochastic and deterministic methods, Hydrological Sciences Journal, 53 (1), 142–164, doi:10.1623/hysj.53.1.142, 2008.
2. D. Koutsoyiannis, A. Montanari, H. F. Lins, and T.A. Cohn, Climate, hydrology and freshwater: towards an interactive incorporation of hydrological experience into climate research—DISCUSSION of “The implications of projected climate change for freshwater resources and their management”, Hydrological Sciences Journal, 54 (2), 394–405, doi:10.1623/hysj.54.2.394, 2009.
3. D. Koutsoyiannis, Hydrology and Change, Hydrological Sciences Journal, 58 (6), 1177–1197, doi:10.1080/02626667.2013.804626, 2013.
4. D. Koutsoyiannis, Stochastics of Hydroclimatic Extremes - A Cool Look at Risk, Edition 3, ISBN: 978-618-85370-0-2, 391 pages, doi:10.57713/kallipos-1, Kallipos Open Academic Editions, Athens, 2023.